圆锥曲线上的数字签名和数字签密

发布时间：2018-06-11 19:24

本文选题：圆锥曲线 + 数字签名　；参考：《西安电子科技大学》2014年博士论文

【摘要】：公钥密码学的提出是密码科学史上的一次重要改革,它解决了对称密码中最困难的两个问题:密钥分配和数字签名。公钥密码算法的最大特点是采用两个相关密钥将加密和解密能力分开,而该算法在已知密码算法和加密密钥,求解解密密钥在计算上是不可行的。消息认证的作用是保护通信双方以防第三方的攻击,然而却不能保护通信双方中的一方防止另一方的欺骗或伪造。通信双方之间也可能存在多种形式的欺骗,因此在收发双方未建立起完全的信任关系且存在厉害冲突的情况下,单纯的消息认证就显得不够,数字签名技术则可有效地解决这一问题。数字签名是一种实现消息或文件认证性的密码技术,其主要目的是用来保证信息的真实性和信息来源的可靠性,并且一个有效的签名能够使消息接收方验证签名者的身份、签名日期和被签名的消息。数字签密技术是一种集加密和签名两种功能于一体的密码体制,即在网络信息传输中同时保证了信息的机密性和可认证性。在签密技术出现以前,用来同时实现保密性和认证性的传统方法是先签名再加密。但是这带来两个问题:效率较低以及有可能降低方案的安全性。签密作为一种新技术,它巧妙地将加密和签名整合到一起,以小于先签名再加密的代价同时实现了对消息的保密性和认证性,同时在计算时间和存储空间上,代价都有所降低。将具有特殊性质的数字签名和签密结合起来便可以得到一些具有特殊性质的数字签密,因而目前签密技术的发展已经引起了众多密码学者的极大兴趣。基于正整数环Zn上的圆锥曲线是一个新型的代数曲线,其特点是明文容易嵌入,同时也易于从曲线中恢复明文,点的运算简单,尤其是求逆简单快速,曲线群的阶容易计算。结合这些特点,在近几年的密码学中圆锥曲线的密码特征逐渐得到了发展和完善,不但一些著名的数字签名可在圆锥曲线上得以实现,而且还表明圆锥曲线上的这些方案相比于有限域上的数字签名方案具有更加完善的密码特征。例如,圆锥曲线上的RSA签名相比有限域上的RSA能抵抗小私钥攻击。基于此,各种性质的数字签名和数字签密在圆锥曲线上相继都得到了实现和数字模拟。本论文对正整数环Zn上的圆锥曲线的密码性质进行了进一步研究,结合圆锥曲线上的密码技术设计了一些高效安全的具有特殊性质的数字签名和数字签密,具体的内容包括以下成果:1.利用圆锥曲线上的公钥密码设计了一个高效的同时生效签名方案。与有限域上的同时生效签名方案相比,所提方案具有运算简单快速,计算量小,有效提高了运算效率,而且在随机预言模型下证明了方案在基于圆锥曲线上的离散对数和大整数分解困难问题下满足不可伪造性、模糊性、公平性。2.利用圆锥曲线上的公钥密码设计了一个高效的完美同时生效签名方案。方案的优势在于利用协议双方建立一个共享的私密钥,并将该私密钥和消息进行绑定,克服了单纯的同时生效签名方案中因起始签名者利用主私钥所引发的不公平因素。3.利用无证书签名思想提出了一个有效的指定验证者的签名方案。与现有的方案相比,方案在保证安全性的同时,减少了信息运算量,改进了方案的运算效率,并在随机预言模型下证明方案满足存在性不可行伪造。4.利用圆锥曲线上的公钥密码签名技术提出了一个公平的无可信第三方的电子信息交换协议。与现有方案相比,方案将信息的交互次数由n+1次降到了3次,有效提高了网络运算效率,降低了通信代价。5.利用圆锥曲线上的公钥密码技术提出了广播签密方案和高效的多重签密方案。和现有的方案相比,所提方案均在运算效率上实现了极大的改进,并在随机预言模型下证明了消息的保密性和不可伪造性。
[Abstract]:The presentation of public key cryptography is an important reform in the history of cryptography. It solves two most difficult problems in symmetric ciphers: key distribution and digital signature. The largest feature of public key cryptography is to separate the encryption and decryption capabilities by using two related keys, and the algorithm is used to solve decryption in known cryptographic algorithms and encryption keys. The key is not feasible in computing. The function of message authentication is to protect the two parties to prevent the attack of third parties, but it can not protect one party from the two parties to prevent the other from cheating or forgery. There may be many forms of deception between the two parties. Therefore, there is no complete trust relationship between the two parties in the transceiver and the existence of the two parties. In the case of severe conflict, simple message authentication is not enough, and digital signature technology can effectively solve this problem. Digital signature is a cryptographic technology that implements message or document authentication. Its main purpose is to ensure the authenticity of information and the reliability of the source of information, and an effective signature can make a message. The receiver verifies the identity of the signer, the signature date and the signed message. The digital signcryption technique is a cryptographic system that combines two functions of encryption and signature, that is, to ensure the confidentiality and authentication of the information in the transmission of network information. The traditional method is to sign and then encrypt. But this brings two problems: low efficiency and possibility of reducing the security of the scheme. As a new technique, signcryption combines encryption and signature ingeniously to realize the confidentiality and authentication of the message at the cost of less than the first signature and reencryption, while calculating the time and storage. With the combination of digital signatures and signatures with special properties, some digital signatures with special properties can be obtained. Therefore, the development of signcryption technology has aroused great interest of many cryptography scholars. The conic curve based on the positive integer ring Zn is a new algebraic curve. The characteristic is that the plaintext is easy to be embedded, and it is easy to recover the plaintext from the curve, and the operation of the point is simple. In particular, the order of the curve group is easy to calculate. Combining these characteristics, the cryptographic features of the conical curve have been developed and perfected in the cryptography in recent years, and not only some famous digital signatures can be conic in conical curves. It is realized on the line and also shows that these schemes have more perfect cryptographic features compared to the digital signature schemes on the finite field. For example, the RSA signature on the conic curve can resist the small private key attack compared to the RSA on the finite field. Based on this, the digital signatures and digital signatures of various properties are successively on the conic curve. In this paper, the cryptographic properties of the conic curve on the positive integer ring Zn are further studied in this paper. Some efficient and secure digital signatures and digital signatures with special properties are designed with the cryptographic technique on the conic curve. The specific contents include the following results: 1. the public key on conic curves is used. A efficient signature scheme with effective simultaneous signature is designed. Compared with the simultaneous effective signature scheme on the finite field, the proposed scheme has simple and fast computation, less computation and efficient operation. Moreover, under the random oracle model, the scheme is proved under the difficult problem of discrete logarithm and large integer decomposition based on the conic line. To satisfy the non forgery, fuzziness and fairness,.2. uses the public key cryptography on the conic curve to design an efficient and perfect simultaneous signature scheme. The advantage of the scheme is to use the two parties to establish a shared private key, and bind the secret key and message, and overcome the beginning of the simple simultaneous signature scheme. The unfairness factor.3. caused by the main private key is used by the signer to use the idea of certificateless signature to propose an effective signature scheme for the designated verifier. Compared with the existing scheme, the scheme reduces the amount of information operation while ensuring the security, improves the operational efficiency of the scheme, and proves that the scheme satisfies the scheme under the random oracle model. A fair and untrusted third party electronic information exchange protocol is proposed by the public key cryptosystem on the conic curve. Compared with the existing scheme, the scheme reduces the number of information interacts from n+1 times to 3 times, effectively improves the efficiency of the network operation and reduces the communication cost.5. using the conic curve, and reduces the communication cost.5.. Public key cryptography proposes the broadcast signcryption scheme and the efficient multiple signcryption scheme. Compared with the existing schemes, the proposed schemes have greatly improved the operational efficiency and proved the confidentiality and the non Forgability of the message under the random oracle model.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.4

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